Topics in Ship Structures
01 Fatigue Strength
Reference : 선박해양구조역학 by 고대은 장범선
Fatigue Strength of Welded Stricutres
DNV 30.7 and DNV RP-C 203
2017.09
Naval Architecture and Ocean Engineering
Jang, Beom Seon
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Introduction
Stress Concentration

2
Different S-N curves for different stress concentrations.
 Stress concentration due to discontinuity or
change of shape.
 Under static loading, a stress concentration
in a ductile material has no effect on the
strength.
Effect of stress concentration
on fatigue strength
2
Stress concentration at increase
of section
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Introduction
Stress concentration caused by weld shape
 Stress concentration level depending on geometric transition,
smooth transition vs. abrupt change
 Concentration at the ‘toes’ of weld is the most likely site.
 Weld surface irregularities, like weld ripples, and lumps.
Stress concentration at toe of weld bead
Comparison of butt and fillet weld shape
Fatigue cracking from weld ripples, and stop/start positions
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Introduction
4
Alternate Stress and Mean Stress
 Stress range
   max   min
 Stress amplitude  a 
 max   min
2
 max   min
 Mean stress
m 
 Stress Ratio
 min
R
 max
2
 For Example
Fully reversed
 Fully reversed
 min   max , R  1,   2 max ,  mean  0
 Zero to max
 min  0, R  0,    max ,  mean   max / 2
Zero to max
 Zero to min
 max  0, R  ,    min ,  mean   min / 2
Zero Structural
to min Lab
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Introduction
Definition of Three Kinds of Stresses



Nominal stress
 A stress to be calculated using general theories such as beam theory.
 It is difficult to consider stress concentration caused by geometric discontinuity.
Hotspot stress (Geometric stress)
 A stress on the surface at hot spot. Not real stress.
 The effect of structural details are taken into account but, the effect of weld bead
is not included.
 To be calculated from shell FE model where weld bead is not included.
Notch stress
 Total stress taking into account the stress concentration caused by the weld bead
and geometric discontinuity.
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Introduction
6
Fatigue Fracture

Three stages of fatigue failure
1) Crack Initiation :
 plastic deformation is accumulated at the toe of weld bead or notch
 Fatigue crack initiates from crack-like flaws and crack growth phase
accounts for 90% of entire fatigue life for welded joint.
2) Crack growth :
 Crack grows perpendicular to principal stress direction.
 Crack growth at crack tip depends on the stress level of crack tip. Crack
always grows under cyclic tensile load.
 Under compressive load, two faces contact and crack tip is closed
3) Final failure : brittle facture, ductile fracture, plastic collapse
Notch crack
propagation under
tensile load
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Introduction
S-N curve
7
 S-N Curve : Relationship curve between stress range () and number of
stress cycles (N) in log-log scale graph.
 Mean S-N curve
1
1
log    log N  log a
m
m
 Design S-N curve
 Survival limit of 97.7% and
failure probability of 2.3%
1
1
log    log N  (log a  2 log s )
m
m
1
1
a
  log N  log a, a  2
m
m
s
s : standard deviation of log N

1
:
m
slope of S-N curve, m=3,4,5
S-N curve
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Introduction
S-N curve


8
S-N curve depends on the level of stress concentration
S-N curve is inversely proportional to cubic of stress range.
log   
1
1
log N  log a
m
m
N  a   m
Example of S-N Curve for three types
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Introduction
Fatigue Test
9
 Cyclic load of 5-15Hz under mean tensile stress to avoid buckling
failure if possible.
 8-24 days for 107 cycles.
 Variations due different weld bead shape.
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Fatigue Failure at Weld Bead
Stress concentration caused by discontinuity


Stress concentration at the edge of a hole
≈ that of Weld toe, but, geometry of weld
toe is different.
Features of weld toe
•
•
Undercutting or abrupt & convex profile,
very small crack-like discontinuities, termed
“ intrusions”.
• Variations along welding length
→ Kt calculation or experimental technique
are meaningless.
Unfavourable characteristics of
weld profiles
104
Comparison of fatigue strengths
Fatigue cracking from pre-existing
crack-like flaw
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Fatigue Failure at Weld Bead
Stress concentration caused by discontinuity



Welded details : Smaller portion of fatigue crack initiation time than
unwelded details. Crack propagation time is dominant.
It is essential that welds are made in accordance with strict procedure.
Weld root fatigue : more severe than weld toe since it is hard to be detected.
Difference between plate and
welded joint
Fatigue cracking from the root
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Factors affecting on Fatigue of Welded Joints
MATERIAL PROPERTY
12
 The fatigue strength of unwelded components increases with
material strength.
 However, this is not the case with welded material. ← crack
propagation of crack-life flaws is dominant and the rate of crack
growth is little affected by material strength
► Use of high-tensile steel (‘70~’80)→ high applied stress → fatigue
crack → high repair cost → cap on the use
→ the same S-N curve as that for mild steel
 Brittle material (fracture failure
with small crack) : little affected.
← fatigue crack growth rate
increases exponentially and the
crack size at final failure doesn't
not have a large influence on
fatigue life.
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Effect of steel strength on
fatigue strength
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Factors affecting on Fatigue of Welded Joints
Weld quality
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 Welding flaws like porosity(다공성), slag, intrusions, lack of fusion,
or incomplete weld root penetration reduces fatigue strength.
 Alternative sites for fatigue crack initiation.
 Misalignment like axial eccentricity or angular distortion subjected to
perpendicular load. → local secondary bending → stress increases.
 Strict welding procedure
 Fitness-for-purpose : estimation of
effect of welding flaws and welding
imperfection
→ establishment of acceptance
limit
(a) Axial eccentricity
(b) Angular distortion
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Factors affecting on Fatigue of Welded Joints
Residual Stress
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 Two systems of stress in welded stresses
1)Reaction stress : from assembly conditions, affecting the various
members as whole.
2) Residual stresses : from weld heating and cooling, affecting localized
area, along welding line.
 During cooling stage the longitudinal shrinkage of the weld metal is
resisted. → high residual tensile stress acting along the welding line
remains at weld joint.
Formation of residual stress
(a) Shrinkage of unrestrained weld
(b) Shrinkage of restrained weld
Typical residual stress distribution
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Factors affecting on Faigue of Welded Joints
Residual Stress


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Behavior of longitudinal residual stresses subjected to a nominal tensile
stress max in the welding direction
Local plastic straining occurs and the stress in the weld remains at 
YS .When load is removed, the stress at the weld becomes  YS -max .
- YS
 YS -max
max
max
 YS

Mechanism of shake down :
•
•
Residual stress at weld toe is usually in the level of yield stress.
Residual stress at weld toe changes during cyclic loading.
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Factors affecting on Faigue of Welded Joints
Residual Stress



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Tensile residual stresses can lead to a reduction of fatigue life.
Tensile cyclic load 0~ max → shifted to  YS - max ~  YS (Tensile)
Compressive cyclic load -  YS ~0→shifted to  YS -max ~  YS(Tensile).
Effective stress from superposition of
applied and residual stress
Superposition of applied stress
and residual stress
Fatigue test results for fillet joints
containing
high tensile
residual stress
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Factors affecting on Faigue of Welded Joints
In Practical Engineering in Ship and offshore field
 Residual stress effect in marine & offshore field?
•
•
•
•
Varying stress amplitude
High stress beyond yield stress due to stress concentration
Shake down effect
Quite complicated especially at bracket toe end
→ Residual stress disappears soon after operation
→ Usually not considered
 Mean stress effect in marine & offshore field?
• Beneficial effect due to compressive mean stress is included.
• Some offshore regulations neglects it in a conservative way.
• Mean stress is calculated in static loading condition.
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Factors affecting on Faigue of Welded Joints
Size effects
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 The effect of weld bead width is
analogous to attachment length.
 The effect of plate width is also significant.
 An appropriate correction factors to
experiment data relevant to other
dimensions.
Dimensions relevant to size effects in
fillet and butt weld joints
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Influence of plate width on stress
concentration
factor
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Factors affecting on Faigue of Welded Joints
Thickness effects





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Fatigue strength decreases with plate thickness.
There exists larger probability of weld flaws in thicker plate.
The number and severity of flaws is likely increase with size.
More restriction on thick plate during the fabrication process
Smaller stress gradient over plate thickness in thicker plate 
larger high stress zone.
Thickness effect due to the stress gradient over
plate thickness
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Ch.3 Factors affecting on Faigue of Welded Joints
Size effects
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 S-N curve representing size effect
Influence of attachment length
Influence of plate thickness
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FATIGUE OF WELDED JOINTS
Transverse butt welds





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Ductile failure occurs in the parent material. No reduction in strength caused
by the weld
Under fatigue loading, stress concentration associated weld reduces fatigue
strength, the effect of stress concentration and weld toe intrusions.
Complete removal of the excess weld metal and weld toe instructions by
machining or grinding.
Variations in shape of weld profiles → Large variation of fatigue life.
Welds which have a minimum of excess metal and a smooth transition at
the weld gives the highest fatigue strengths.
Single sided
Butt welding
Double sided
Butt welding
Fatigue failure from the toe of a transverse
butt weld
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FATIGUE OF WELDED JOINTS
Transverse butt welds (Both sides)- Misalignment
b 
3e
 a
T
 a   b   a (1 
3e
3e
), K g  (1  )
T
T
Kg=Stress concentration factor
Local stress range Kg a
 Angular misalignment 1° , Kg= 0.3
Nominal stress range
 Axial misalignment
 Local bending stress, a = nominal applied axial stress
Effect of weld profile on fatigue
strength of transverse butt welds
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Fatigue test results from axially
misalignedStructural
butt welds
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FATIGUE OF WELDED JOINTS
Transverse butt welds – Single Sided butt welds
 Single sided welds : pipes or rectangular or circular
hollow section.
 Lack of penetration or unfavorable bead shape with a
bad profile → low fatigue strength
 Backing strip is effective.
Use of ceramic backing
strip
Root cracks of butt welds
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FATIGUE OF WELDED JOINTS
Transverse butt welds – Single Sided butt welds
 Permanent backing :
 integral with one of the members.
 crack initiation at the junction of the weld metal and backing strip.
 useful to tubular component.
To be machined out
Fatigue failure in transverse butt weld
made on backing strip
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FATIGUE OF WELDED JOINTS
Transverse butt welds – S-N Curve
Detail
Sketch of detail
Transverse butt welds
with good profile
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105 cycles
2x106
355 MPa
155 MPa
310 MPa
155 MPa
Transverse butt weld
with poorer profile
(including submerged
arc)
260 MPa
116 MPa
Transverse butt weld
on a permanent
backing strip
260 MPa
115 MPa
Transverse electron
beam butt weld
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FATIGUE OF WELDED JOINTS
Longitudinal butt Welds




26
The excess weld metal lies parallel to the direction of applied load → no
stress concentration.
Stop/start positions, where the electrode is changed in manual welds, the
ripples on the surface.
Far less severe than that at the edge of the excess weld metal in transverse
direction.
Side plates produce severe stress concentration.
Fatigue cracking at the attachment
butt welded to edge of stressed plate
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Fatigue cracking from weld ripples, (b)
Stop/start
positions
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FATIGUE OF WELDED JOINTS
Longitudinal butt Welds – S-N Curve
Detail
Sketch of detail
27
105 cycles
2x106
Plain as-rolled steel
plate
300 MPa
200 MPa
Continuous automatic
longitudinal weld
350 MPa
160 MPa
Continuous manual
longitudinal weld
325 MPa
140 MPa
Longitudinal butt weld
on tack welded
backing strip
280 MPa
125 MPa
260 MPa
120 MPa
Intermittent longi.
Fillet weld
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FATIGUE OF WELDED JOINTS
Longitudinal butt Welds – S-N Curve
Detail
Sketch of detail
28
105 cycles
2x106
Web/flange weld at
cope hole
230 MPa
95 MPa
Fillet attachment to
edges of stresses
members
180 MPa
70 MPa
Butt attachment to
edges of stresses
members
180 MPa
70 MPa
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FATIGUE OF WELDED JOINTS
Fillet Welded Connections
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 Attachments give rise to a general stress concentration in addition to
local effect of the weld.
 Non-load-carrying fillet weld : attachment welds not designed to
transmit the loads.
 Load-carrying fillet weld : transmits load from one member to
another.
 Some loads will be transmitted through non-load carrying joint.
Fillet welded
attachment
Non-load carrying
Fillet weld
Lug : load carrying
member to lifting load,
but non-load carrying
member to bending
stress
Load carrying
Fillet weld
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FATIGUE OF WELDED JOINTS
Fillet Welded Connection – Non load carrying
 Stress concentration increases with increase in attachment
length, ’L’, the thickness of longitudinal attachment or the width of
doubling plate.
 Increase in main plate thickness can lead to a reduction in fatigue
strength.
 Crack initiates at weld toe end and propagate through the plate.
Examples of non-load carrying fillet welded attachment
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FATIGUE OF WELDED JOINTS
Fillet Welded Connection – Non load carrying
 Hard to detect through visual inspection, dye penetrant is
used.
Fatigue cracking at toe of transverse fillet weld (5.5 mm crack depth)
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FATIGUE OF WELDED JOINTS
Fillet Welded Connection – Non load carrying
 Attachment with single fillet weld : fatigue crack initiation at crack
root.
 Weld root crack is unlikely to be detected before final failure. No
measures to improve the fatigue strength by treating the weld toe.
 To return the ends of the weld around the
edge of the attachment → little
improvement of fatigue strength but,
sealing against corrosion.
Transverse attachment
welded from one side
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Fatigue failure from end of
longitudinal
fillet weld Structural Lab
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FATIGUE OF WELDED JOINTS
Fillet Welded Connection – Non load carrying
 Continuation of the weld around the ends of the edge type of
attachment and across the edge of the main plate.
→ adversely reduce fatigue strength due to larger geometric
discontinuity.
Fatigue strength = 70 MPa at
2X106 cycle
Fatigue strength = 52 MPa at
2X106 cycle
Fatigue cracking from end of fillet welded
attachment to edge of stressed plate
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FATIGUE OF WELDED JOINTS
Fillet Welded Connection – Non load carrying
Detail
Sketch of detail
105 cycles
34
2x106
Fillet or butt welded
stiffeners or
attachments to the
surfaces of stresses
member
250
95
Cover plates on beam
flanges
160
65
Web/flange weld at
cope hole
230
95
Butt welded
attachments to the
edges of stressed
member
180
70
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FATIGUE OF WELDED JOINTS
Fillet Welded Connection – Non load carrying
 Intermittent fillet welds joining web to a flange in a beam : the
geometric stress concentration, fatigue strength is slightly high. =
120 MPa at 2X106 cycle.
 Web/flange fillet weld at cope hole : stress concentration is
increased.
Web
Fillet
Fatigue cracking from the end of a longi.
intermittent web/flange fillet weld.
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Fatigue cracking from the end of a
web/flange fillet weld at cope hole.
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FATIGUE OF WELDED JOINTS
Fillet Welded Connection – Load carrying fillet welds

Design of load carrying fillet welded joints for static loads
•
•
•

Weld length H is determined such that P/2AW< allowable design stress
Fig (a) : 2AW/AP =1, the same stress in both the plate and the weld < allowable
tensile stress (H =0.7B)
Fig (b) : P/(total weld length X 4 throat thickness ) < allowable shear stress
However, behavior under Fatigue loading condition is more complicated.
Fatigue strengths are dependent on weld configurations and joint forms
σw=P/2AW
Aw
σP=P/AP
Ap
Fig (a) Transverse load-carrying fillet weld
Fig (b) Longitudinal load-carrying fillet weld
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FATIGUE OF WELDED JOINTS
Fillet Welded Connection – Load carrying fillet welds



37
The location of failure depends on the ratio leg length/plate thickness (H/B) .
Fatigue strength at weld toe = 85 MPa at 2X106
at weld root = 57 MPa at 2X106
For the same fatigue life at weld toe and weld root,
 p (toe ) 2 Aw
2 H 85



 1.5
 w( root )
AP
B
57
1.5 B
H
 1.06 B
2
 Optimum performance : enough
weld metal to ensure that
failure would be form the weld
toe rather than weld root.
σw=P/2Aw
Aw
σP=P/AP
Ap
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FATIGUE OF WELDED JOINTS
Fillet Welded Connection – Load carrying fillet welds



Cruciform joint : two basic stress concentrations : at weld root and at weld
toes.
Large fillet leg length (H1) : Larger notch stress at weld toes and smaller
stress on weld throat → crack initiation at weld toe.
Small fillet leg length (H2) : Larger stress on the weld throat and smaller
stress at weld toe → crack initiation at weld root.
Two possible sites for fatigue cracking
Fatigue cracking for different leg length
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FATIGUE OF WELDED JOINTS
Fillet Welded Connection – Load carrying fillet welds
39
 Partial penetration welds can achieve a given throat dimension with
a leg length smaller than would be required in normal fillet weld.
→ efficient way of improving fatigue performance.
 Full penetration weld eliminates stress concentration at the weld root
and reduce stress concentration at the toes.
→ However, the improvement is limited, increase of 10 MPa at 2X106
Full penetration butt welded cruciform joint
Partial penetration fillet weld
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FATIGUE OF WELDED JOINTS
Fillet Welded Connection – Load carrying fillet welds
 Example of full penetration welds in ship structures
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FATIGUE OF WELDED JOINTS
Fillet Welded Connection – Load carrying fillet welds



41
Misalignment of cruciform joint introduces secondary
bending stress and increases the stress range at the
weld toe and weld root.
Less effect for weld root crack since it is closer to
neutral axis of the section w.r.t. the induced bending
moment.
In real structure, the restraint of cross plate inhibits
bending due to misalignment. (no restraint in test)
Joints failing from the weld toe in the plate
41
Joints failing
from
the weld Structural
root in weld
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FATIGUE OF WELDED JOINTS
Transverse butt welds (Both sides)- Misalignment

Stress concentration factors for butt welds (DNV –RP-C203,2010,Section
3.1.2)
𝐾𝑔 = 1 +
1/2(𝑇2 − 𝑇1 )
6(𝛿𝑚 + 𝛿𝑡 − 𝛿0
𝑇11.5
𝑇1 1 + 1.5
𝑇2
0.1𝑇1
𝑇2
𝑇1
42
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FATIGUE OF WELDED JOINTS
Fillet Welded Connection – Load carrying
Detail
Sketch of detail
105 cycles
43
2x106
Full penetration T or
cruciform joints
360
95
Fillet welded T or
cruciform joints
250
85
Lap joint with
transverse fillets
250
85
Weld throat failure in
transverse weld
(based on stress on
weld throat)
154
57
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FATIGUE OF WELDED JOINTS
Fillet Welded Connection – Root Crack
 Design Chart for fillet and partial penetration welds(DNV –RPC203,2010,Section 2.8)
 Design should be performed such that fatigue cracking from the root
is less likely than from the toe.
Design chart for partial penetration fillet weld (DNV-RP-C203)
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FATIGUE OF WELDED JOINTS
Fillet Welded Connection – Load carrying fillet welds




45
Lap joint using longitudinal fillet weld : less sensitive to weld size since the
changes of section at the weld toe and weld root are parallel with the
direction of applied stress.
Weld ends induce stress concentration in both the main and cover plates.
Weld on the edge is more damaging than weld on surface.
Under the same nominal stress (BXWP=2BCPWCP), failure will initiate from a
weld end and propagate into the cover plate.
Fatigue failure from weld ends in cover plate
Weld
ends
Lap joint made using longi. fillet joint
 Designed
BWP<2BCPWCP
 Continued weld
around the end
Joint45with weld continued
around end
of cover
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Ch. 4 FATIGUE OF WELDED JOINTS
Fillet Welded Connection – Load carrying
Detail
Sketch of detail
105 cycles
46
2x106
Lap Joint with weld
continued around end
of cover plate
235
85
Lap joint with longi.
fillet welds – crack
initiates on surface
230
80
Lap joint with longi.
fillet welds – crack
initiates on edge of
cover plate
200
66
Load carrying weld on
plate edge – not
welded around end
150
50
Load carrying weld on
plate edge – welded
around end
125
44
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Design Regulations
47
What is fatigue failure?

Before 70’s, fatigue strength is not a critical issue to be treated in ship design stage.

Remarkable increase in use of high tensile steel (‘70~’80) → high applied stress →
frequent occurrence of fatigue crack → high repair cost

The fatigue strength of unwelded components (base material) increases with material
yield strength but this is not the case with welded joints ← crack propagation of
crack-like flaws is dominant and the rate of crack growth is little affected by material
strength

During 80’~90s, lots of research in fatigue strength → fatigue strength assessment is
mandatory, cap on the use of high tensile steel is placed by ship owner.

The most common and important failure mode together with buckling.
Demand of fatigue strength assessment based on wave load analysis is increasing,
especially for high risk vessel like LNG carrier. ( Required fatigue life of LNG carrier is
40 years)

Offshore structure requires higher fatigue life than commercial ship due to no
inspection after re-docking (Commercial vessel : 25 years. Offshore structure : 40 ~
200 years depending on the accessibility)
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Design Regulations
48
Fatigue strength assessment
 Assessment of fatigue life under one cyclic load is simple since it
can be predicted from S-N curve.
 However, fatigue damage is accumulated over the entire lifetime of a
vessel, it is hard to analyze the load and stress history.
 Due to a huge number of welded joints in a vessel, an engineering
sense to screen critical joints which are prone to fatigue crack is
important.
 Fatigue analysis using finite element method : construction of
detailed fine mesh model and hot spot stress evaluation under
random wave load are sophisticated work.
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Design Regulations
49
Fatigue Critical Area
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Design Regulations
50
Fatigue Critical Area
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Design Regulations
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Fatigue Critical Area
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Design Regulations
52
Fatigue Critical Area
OPen INteractive Structural Lab
Design Regulations
Fatigue strength assessment : LNG Carrier
Hydrodynamic
Analysis
Full Stochastic
FE analysis
53
Local Zoom
Model
OPen INteractive Structural Lab
Design Regulations
Fatigue strength assessment : LNG Carrier
Hopper
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54
Design Regulations
Fatigue strength assessment : FPSO
OPen INteractive Structural Lab
55
Design Regulations
S-N Curve – DNV RP –C203 vs DNV 30.7 Ship
Rule
OPen INteractive Structural Lab
56
Design Regulations
Nominal Stress based Approach : DNV RP –C203
OPen INteractive Structural Lab
57
Design Regulations
Nominal Stress based Approach : DNV RP –C203
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58
Design Regulations
Nominal Stress based Approach : DNV RP –C203
OPen INteractive Structural Lab
59
Design Regulations
Nominal Stress based Approach : DNV RP –C203
OPen INteractive Structural Lab
60
Design Regulations
Nominal Stress based Approach : DNV RP –C203
OPen INteractive Structural Lab
61
Design Regulations
Nominal stress approach – S-N Curve : DNV RP –C203
 S-N Curves in seawater with cathodic protection
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Design Regulations
Nominal Stress Approach-Combined stress : DNV RP –C203


63
Design Chart for fillet and partial penetration welds
Depending on the angle between principal stress and welding line, different
S-N curves are applied.
Classification E or F
S-N curve depending on stress direction normal to
the weld and crack propagation
Classification C2
OPen INteractive Structural Lab
Design Regulations
64
Hot Spot Stress Approach
 Use of finite element analysis and difficulty in nominal stress → hot
spot stress for fatigue life assessment.
 Linear interpolation from t/2 and 3t/2
 Or σhot spot = Kg∙σnominal, Kg : structural stress concentration factor.
Schematic stress distribution at a hot spot
OPen INteractive Structural Lab
Design Regulations
Hot Spot Stress Approach – Modeling
65
 Shell element modeling :
• Modeling is easy but higher stress than the actual.
• 8-noded element is more flexible than 4-noded → less stress
• t x t mesh size
 Solid element modeling :
• Modeling is quite difficult but close to the actual.
• Fillet weld is modeled.
• 20-noded element is more flexible than 8-noded, t x t mesh size
Different hot spots
Extrapolation in FE
Shell Element Model
Extrapolation in FE
Solid Element Model
OPen INteractive Structural Lab
Design Regulations
Hot Spot Stress Approach–Hot Spot Stress
 Derivation of stress at read out points 0.5 t and 1.5 t
 If mesh size is t x t in shell element, top surface stress to be read at
mid side nodes along A-B
 If solid element, stress to be extrapolated to the surface.
 If element size > t, fit a second order polynomial to the element
stresses in the three first elements and derive 0.5t & 1.5t stresses.
Extrapolated hot
spot stress
Intersection
line
Hot Spot
Gaussian integration point
Example of derivation of hot spot stress
Derivation of hot spot stress for
element
size
larger than
t x tLab
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INteractive
Structural
66
Design Regulations
Hot Spot Stress Approach – S-N Curve : DNV RP-C203
Stress range (MPa)
 D Curve in air
Number of cycles
S-N curves in air
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67
Design Regulations
Hot Spot Stress Approach – S-N Curve : DNV RP-C203
 Relationship between S-N Curves
D – curve, SCF=1.0
log N  12.164  3.0 log 
F1 curve, SCF=1.43
log N  12.164  3.0 log( SCF ( 1.43)   )
 11.699  3.0 log 
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68
Design Regulations
Hot Spot Stress Approach – S-N Curve : DNV CN.30.7
 Relationship between S-N Curves
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69
Design Regulations
Hot Spot Stress Approach – S-N Curve : DNV CN.30.7

Stiffener support is used to mitigate stress concentration at the intersection
between stiffener flange and web section .
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70
Design Regulations
Hot Spot Stress Approach – S-N Curve : DNV CN.30.7


Fatigue crack at lower hopper knuckles is caused by external dynamic
pressure and internal dynamic pressure of ballast tank or cargo tank.
Fatigue crack initiates on inner bottom plate and propagates along the
welding line.
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71
Design Regulations
Notch Stress Approach
72
 Effective notch stress is the total stress at the root of a notch, obtained assuming
linear-elastic material behaviour.
 For structural steels an effective notch root radius of r = 1.0 mm has been
verified to give consistent results.
 The method is restricted to welded joints which are expected to fail from the
weld toe or weld root and it is limited to thicknesses t 5 mm.
 Flank angles of 30° for butt welds and 45° for fillet welds are suggested.
 After certain post weld improvement procedures such as grinding, the actual
geometrical radius may be used in the effective notch stress analysis.
Frank angle and notch radius
Analysis of effective notch stress
OPen INteractive Structural Lab
Design Regulations
Notch Stress Approach



73
Calculation of effective notch stress by the finite element method : a fine
element mesh is used around the notch region.
This maximum surface stress directly from the nodal stress calculated at
the surface or from extrapolation of element stresses to the surface.
The effective notch stress to be used together with the recommended S-N
curve is the maximum calculated surface stress in the notch.
Notch stress based S-N 선도
OPen INteractive Structural Lab
Design Regulations
74
Fatigue Limit



Fatigue limit is the maximum stress range below which the fatigue
strength is infinite.
Permitted in design only when all stress range blocks are below the
fatigue limit.
Otherwise, the slop is reduced from (-1/3) to (-1/5).
Stress cycling where further fatigue
assessment can be omitted
Stress cycling where a detailed
fatigue assessment is required
OPen INteractive Structural Lab
Design Regulations
Mean Stress Effect : DNV RP –C203
 Mean stress influence for non welded structure
 For fatigue analysis of regions in the base material not significantly
affected by residual stresses due to welding, the stress range may be
reduced if part of the stress cycle is in compression.
 t  0.6  c
fm 
t  c
 
,0 
2 
 

 c  compressive stress  min 0,  static 

2




 t  tension stress  max  static 
log N  log a  m log( f m  )
Stress Range Reduction Factor (fm)
 The calculated stress range may be multiplied with the reduction factor
fm before entering the S-N curve
 For welded joint
 Mean stress effect is neglected for fatigue assessment of welded
connections due to tensile residual stress around welded joint.
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75
Design Regulations
76
Mean Stress Effect : DNV RP –C203
Load Ratio R 
 min
 max
Zero to max
fm =1.0
Fully reversed
R=-1
Mean stress effect on S-N Curve
fm =0.8
Fatigue life is increased by
(1/0.8)3= 1.95 times
Zero to min
m 
 max   min
2
fatigue life 
1
(f m  ) 3
Stress Range Reduction Factor (fm)
fm =0.6
Fatigue life is increased by
(1/0.6)3= 4.63 times
OPen INteractive Structural Lab
Design Regulations
Mean Stress Effect : DNV 30.7 Ship Rule
77
 For Base material
fm 
 t  0.6  c
t  c
 
,0 
2 
 

 c  compressive stress  min 0,  static 

2 



 t  tension stress  max  static 
Stress Range Reduction Factor (fm)
 The calculated stress range may be multiplied with the reduction factor
fm before entering the S-N curve
 For welded joint
 A hot spot region is subjected to tensional residual stress.
 However, residual stresses due to welding and construction are reduced
over time as the ship is subjected to external loading.
 The mean stress effect is applicable. (Slightly larger than Base material)
 t  0.7  c
fm 
t  c
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2 S-N Curve – DNV RP-C203 Offshore Rule
78
Thickness Effect

Basic S-N curve
Tested plate thickness =22mm (DNV 30.7 Ship Rule)
Tested plate thickness =25mm (DNV RP-C203 Offshore Rule)


Surface stress on the weld bead is increasing exponentially
If plate thickness is beyond the reference thickness , modification of S-N curve is
needed.
 t
log N  log a  m log  
t
 ref



k
 t : plate thickness
 k : thickness exponent
DNV RP-C203 : k =0~0.3
DNV CN 30.7 : k=0.25
Stress distribution through thickness
OPen INteractive Structural Lab
Design Regulations
Effect of corrosive environment : DNV RP –C203


Decrease in Fatigue Strength in Corrosive
environment.
Cathodic protection : to control the corrosion of a
metal surface by connecting the metal to be
protected with another more easily corroded
"sacrificial metal" to act as the anode of the
electrochemical cell.
S-N curves in air
S-N curves in seawater with cathodic protection
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79
Design Regulations
Nominal Stress based Approach : DNV RP –C203
 S-N Curves in air
k
S-N Curves in seawater with cathodic protection
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80
Design Regulations
Effect of corrosive environment : DNV CN 30.7


Ship rule is not conservative.
SN-Curve for air = SN-Curve for cathodic protection.
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81
Calculation of Fatigue life
82
Palmgren-Miner rule
 EX) During 10 years, 1 : n1 cycles
2 : n2 cycles
3 : n3 cycles
k
ni
 Damage ratio D 
N
i 1
i
D = n1/N1 + n2/N2 + n3/N3
Fatigue Life= (n1+ n2 + n3)/D = 10 years/D
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Calculation of Fatigue life
83
Palmgren-Miner rule
 Palmgren-Miner Rule
k
k
i 1
i 1
D   Di  
ni
n
n
n
 1  2    k
N i N1 N 2
Nk
Where,
k= number of stress blocks
ni = number of stress cycles in stress block with constant stress range
Ni = number of cycles to failure at constant stress range
L0
D
Lo = the time for the total number of stress cycles
L = fatigue life
L
k
n 0   ni
i 1
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Calculation of Fatigue life
84
Example 1

Calculate fatigue life of the following butt weld using E curve subjected to
long term stress range in sea water in cathodic protection. Use DNV-RPC203. Plate thickness = 40 mm. Mean stress is tensile stress.
 i
 i
OPen INteractive Structural Lab
Calculation of Fatigue life
85
Example 1 : Solution
 It belongs to E class and thickness effect to be considered.
 E class
log a  11.61, m  3 for N  106
log a  15.35, m  5 for N  106
for N  106
t 0 .2
)  m log 
25
40
11.61  3.0 log( ) 0.2  3.0 log 
25
 11.49  3.0 log 
log N  log a  m log(
for N  106
40 0.2
)  5.0 log 
25
 15.15  5.0 log 
log N 15.35  5.0 log(
Damage ratio = 0.247
 Fatigue Life = n0/0.247 =1,664,413
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Calculation of Fatigue life
86
Equivalent Stress Range
 The same tress range is assumed to be applied across the entire life
and it gives the same damage ratio subjected to variable stress
ranges
n
n 
D i  i
, N i  a  i m
a
i 1 N i
i 1
k
k
m
i
 eq
D
 k ni  im 
 

n
0
 i 1

n0  eqm
a
k
, n0   ni
i 1
1/ m
OPen INteractive Structural Lab
Post weld improvement
Weld Toe grinding - mitigation of stress concentration
 A major cause of fatigue damage in welded structures : stress
concentration at the toe + crack-like flaws.
 Machining and grinding to eliminate such flaws and give a smoother
profile → improvement fatigue strength.
 Disc grinding is completely more quickly.
 Hand-held burr grinding is more effective.
Burr machining and disc grinding
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87
Post weld improvement
Weld Toe grinding – mitigation of stress concentration
 Fatigue life improvement is valid only when corrosion protection is
effective
 After protection, corrosion induces notches.
 Adverse effect of strength reduction due to the decrease in area.
As Welded
Burr Ground
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88
Post weld improvement
89
Weld Toe grinding – side effect, corrosion
 Corrosion pitting of the ground metal surface virtually eliminates the
benefit of burr grinding.
 The ground surface must be adequately protected by cathodic
protection system or permanent protection means like a paint
system.
Corrosion pitting
OPen INteractive Structural Lab
Post weld improvement
Weld Toe grinding – mitigation of stress concentration


Necessary to remove all traces of the original weld toe and material to a
depth of 0.5~1.0 mm below any undercut.
0.5mm <Depth of grinding < 2mm or 7% of plate thickness
Depth of grinding
Depth measurement gauge
OPen INteractive Structural Lab
90
Post weld improvement
TIG dressing
91
 TIG and plasma dressing




As effective as local grinding but considerably faster.
To re-melt the weld toe and wash the weld pool into the plate surface as to
produce a smoother weld profile and remove inherent flaws.
TIG dressing calls for precise positioning of the arc
Plasma technique gives a larger area of heating → less demanding
Weld cross section
91
Influence of electrode position fatigue
strength
plasma dressed
filletLab
welds
OPenofINteractive
Structural
Post weld improvement
Weld Toe grinding - Burr Grinding





92
A high speed pneumatic, hydraulic or electric grinder : rotational
speed :15,000 ~ 40,000 rpm.
The diameter :10 ~ 25 mm for 10t ~50t.
root radius > 0.25t.
The high-speed grinding tool removes material at a high rate.
The cutting operation itself produces hot, sharp cuttings and some noise.
Heavy protective clothing together with leather gloves, safety glasses and
ear protection are mandatory
Pneumatic grinder and burrs
Example of protective clothing
used during weld toe burr grinding.
OPen INteractive Structural Lab
Post weld improvement
Hammer peening - compressive residual stress



Effective stress = applied stress + residual stress
Tensile residual stress + compressive applied stress = no compressive
mean stress effect
Compressive residual stress + tensile applied stress = compressive mean
stress effect


Superimposition of applied
and residual stresses
High compressive stresses at the site of stress
concentration leads to an improvement in
fatigue strength.
Cold working the material surface →
compressive stress on surface which is
balanced by a residual tensile stress within
core.
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93
Post weld improvement
Hammer peening - compressive residual stress
 Hammer peening


pneumatic or electric hammer with round-ended tool → compressive stress
on the surface of stress concentration
Noise problem : sometimes not allowed for health reasons → Needle
peening
Hammer peeing fillet weld toe
Needle peeing fillet weld toe
Weld cross-section
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94
Post weld improvement
Hammer peening - Equipment
 Suitable pneumatic hammer gun has a 15 to 30 mm diameter piston,
operates at an air pressure of 5 to 7 bars and delivers 25 to 100
blows per second. Impact energy is typically in the range 5 to 15
Joules.
 The weight of the gun is from about 1 to 3.5 kg.
 Hammer peening have made use of hammer gun, both of which are
primarily intended for use as chipping (쪼다) hammers.
Pneumatic riveting guns used for
hammer peening.
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95
Post weld improvement
Hammer Peening - Procedure
96
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Post weld improvement
Effects of Post Weld Improvement
97
 Comparison of post weld improvement methods
Improvement of S-N curve
OPen INteractive Structural Lab
Post weld improvement
Improvement of Fatigue Life by Fabrication DNV RP-C203
 Grinding should extend below the plate surface by a rotary burr.
 The grinding depth should not exceed min (2 mm, 7% of the plate
thickness).
 A good design practice to exclude this factor at the design stage and
to keep the possibility of fatigue life improvement as a reserve.
 Crack grows faster after initiation → shorter inspection intervals
during service life in order to detect the cracks before they become
dangerous.
Grinding of welds
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98
Post weld improvement
Improvement of Fatigue Life by Fabrication DNV RP-C203
 Improvement on fatigue life by different methods
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99
Calculation of Fatigue life -Post weld improvement
Example 2

100
The following welded joint is subjected to cyclic load which gives the
following nominal stress range during 10 years in seawater with
cathodic protection in accordance with DNV RP-C203
Applied nominal
stress range (MPa)
70
80
90
100
110





Number of
applied cycles
5.0X105
4.0X105
3.0X105
2.0X105
1.5X105
Principal stress direction (f) = 40 degrees
Plate thickness = 30 mm
Static nominal mean stress : 20 MPa (Tensile stress)
Steel : High Tensile steel (Yield stress = 355 MPa)
Weld toe grinding is applied.
OPen INteractive Structural Lab
Calculation of Fatigue life -Post weld improvement
Example 2 : Solution
101
 Principal stress direction (f) = 40 degrees
 Plate thickness = 30 mm
t>25
45
60
30
  t  0.20 
log N  log a  m log    
  25  


  t  0.20 
log N  11.610  3.0 log     N  106
  25  


  t  0.20 
log N  15.350  5.0 log     N  106
  25  


OPen INteractive Structural Lab
Calculation of Fatigue life -Post weld improvement
Example 2 : Solution
102
Stress range (MPa)
 E Curve
Number of cycles
OPen INteractive Structural Lab
Calculation of Fatigue life -Post weld improvement
Example 2 : Solution
103
 Static nominal mean stress : 20 MPa (Tensile stress)
→ Mean stress effect is not allowed in DNV RP-C203.
 Fatigue Damage Calculation
Δσnominal
70
ni
500,000
Ni
1,110,014
Di
0.45044
Remarks
6
Use N>10 curve
6
80
400,000
713,216
0.56084
Use N<10 curve
90
300,000
500,915
0.59890
Use N<106 curve
100
200,000
365,167
0.54769
Use N<106 curve
110
150,000
274,355
0.54674
Use N<106 curve
D=
2.705
For N  106
  t  0.20 
log N  11.610  3.0 log    
  25  


6
For N  10
  t  0.20 
log N  15.350  5.0 log    
  25  


Fatigue Life = 10 year / 2.705 = 3.7 year
 Steel : High Tensile steel (Yield stress = 355 MPa)
 Weld toe grinding is applied.
Post Improvement : yield stress > 350 MPa , Improvement on fatigue life = 3.5
Fatigue Life = 3.7 year X 3.5 = 13.0 years
OPen INteractive Structural Lab
Calculation of Fatigue life -Post weld improvement
Example 3
104

The following welded joint is subjected to cyclic load which gives the
following hotspot stress range during 20 years in seawater with
cathodic protection in accordance with DNV CN-30.7




Plate thickness = 30 mm
Static nominal mean stress : 20 MPa (Tensile stress)
Steel : High Tensile steel (Yield stress = 355 MPa)
Weld toe grinding is applied.
OPen INteractive Structural Lab
Calculation of Fatigue life -Post weld improvement
Example 3 : Solution
105
 Static nominal mean stress : 20 MPa (Tensile stress)
fm 
 t  0.7  c
t  c
 t  tensile stress  max( static   / 2,0)
 c  compressive stress  min(0,  static   / 2)
 Fatigue Damage Calculation
For N  106
0.25

 t  
log N  12.164  3.0 log  f m    

 25  

For N  106
0.25

 t  
log N  15.606  5.0 log  f m    

 25  

Fatigue Life = 20 year / 2.63 = 7.61 year
 Steel : High Tensile steel (Yield stress = 355 MPa)
 Weld toe grinding is applied.
Post Improvement : yield stress > 350 MPa , Improvement on fatigue life = 3.5
Fatigue Life = 7.61 year X 3.5 = 26.63 years
OPen INteractive Structural Lab